留言板

尊敬的读者、作者、审稿人, 关于本刊的投稿、审稿、编辑和出版的任何问题, 您可以本页添加留言。我们将尽快给您答复。谢谢您的支持!

姓名
邮箱
手机号码
标题
留言内容
验证码

有限元法求解瞬态温度场时的数值振荡研究

刘文胜 李璇 马运柱 杨肃

刘文胜, 李璇, 马运柱, 杨肃. 有限元法求解瞬态温度场时的数值振荡研究[J]. 应用数学和力学, 2018, 39(4): 403-414. doi: 10.21656/1000-0887.380166
引用本文: 刘文胜, 李璇, 马运柱, 杨肃. 有限元法求解瞬态温度场时的数值振荡研究[J]. 应用数学和力学, 2018, 39(4): 403-414. doi: 10.21656/1000-0887.380166
LIU Wensheng, LIXuan, MA Yunzhu, YANG Su. Study of Numerical Oscillation in Solving Transient Temperature Fields With the Finite Element Method[J]. Applied Mathematics and Mechanics, 2018, 39(4): 403-414. doi: 10.21656/1000-0887.380166
Citation: LIU Wensheng, LIXuan, MA Yunzhu, YANG Su. Study of Numerical Oscillation in Solving Transient Temperature Fields With the Finite Element Method[J]. Applied Mathematics and Mechanics, 2018, 39(4): 403-414. doi: 10.21656/1000-0887.380166

有限元法求解瞬态温度场时的数值振荡研究

doi: 10.21656/1000-0887.380166
基金项目: 国家高技术研究发展计划(863计划)(2009AA034300)
详细信息
    作者简介:

    刘文胜(1967—),男,教授,博士生导师;马运柱(1975—),男,教授,博士生导师(通讯作者. E-mail: yangsupm@csu.edu.cn).

  • 中图分类号: TK124

Study of Numerical Oscillation in Solving Transient Temperature Fields With the Finite Element Method

Funds: The National High-tech R&D Program of China (863 Program) (2009AA034300)
  • 摘要: 针对有限元求解瞬态温度场时解的振荡问题,通过对热传导矩阵和热容矩阵的分析,研究了数值仿真中解的振荡原因以及消除振荡的方法.研究结果表明,热传导矩阵违反了热力学第二定律以及在迭代初期,协调热容矩阵的单元内温度变化率的连续性假设与实际偏差很大是产生数值振荡的原因.规范单元形状和采用适当的集中热容矩阵,可以有效消除数值振荡.同时,以无限大平板传热过程为背景,通过不同计算方法的对比,验证分析了结论.
  • [1] 马向平, 骆清国. 瞬态温度场有限元法求解的研究[J]. 装甲兵工程学院学报, 2002,16(2): 22-26.(MA Xiangping, LUO Qingguo. The investigation of a finite element analysis and solution of the transient temperature field[J]. Journal of Armored Force Engineering Institute,2002,16(2): 22-26.(in Chinese))
    [2] 刘刚, 李长生, 刘相华. 有限元法求解瞬态温度场时的振荡问题[J]. 钢铁研究学报, 2008,20(7): 19-22.(LIU Gang, LI Changsheng, LIU Xianghua. Oscillation problem during solving for transient temperature field using FEM[J]. Journal of Iron and Steel Research,2008,20(7): 19-22.(in Chinese))
    [3] 杨汇涛, 韩振兴. 加权变系数的瞬态导热有限元法[J]. 航空动力学报, 1997,12(1): 95-97.(YANG Huitao, HAN Zhenxing. A finite element analysis of transient heat conduction with weighted variable factor[J]. Journal of Aeronautical Power,1997,12(1): 95-97.(in Chinese))
    [4] 林金木. 瞬态温度场的解及其振荡[J]. 工程热物理学报, 1996,17(3): 333-337.(LIN Jimu. Solutions and their oscillations in determining of transient temperature fields[J]. Journal of Engineering Thermophysics,1996,17(3): 333-337.(in Chinese))
    [5] 纪崢. 关于瞬态温度场有限元分析中采用协调或集中质量热容矩阵的探讨[J]. 计算结构力学及其应用, 1986,3(2): 35-41.(JI Zheng. Discussion on use of consistent or lumped mass heat capacity matrix in finite element analysis of transient temperature field[J]. Computational structural Mechanics and Applications,1986,3(2): 35-41.(in Chinese))
    [6] 陈罕, 周昆颖. 集中矩阵在传热有限元计算中的应用[J]. 北京化工学院学报(自然科学版), 1991,18(4): 45-51.(CHEN Han, ZHOU Kunying. The use of lumped capacitance matrix in FEM for solving transient heat transfer Problem[J].Journal of Beijing Institute of Chemical Technology,1991,18(4): 45-51.(in Chinese))
    [7] 冯卫星. 单元形状对有限元法计算精度的影响[J]. 数学与科技, 1987(3): 58-62.(FENG Weixing. The Influence of unit shape on the accuracy of finite element method[J]. Mathematics and technology,1987(3): 58-62.(in Chinese))
    [8] 施飞, 程晓民, 张韬杰, 等. 树脂传递成型过程中温度场的数值研究[J]. 应用数学和力学, 2016,37(3): 256-265.(SHI Fei, CHENG Xiaomin, ZHANG Taojie, et al. Numerical research of temperature field during resin transfer molding[J]. Applied Mathematics and Mechanics,2016,37(3): 256-265.(in Chinese))
    [9] 郭延华, 杨建辉, 武浩. 平面有限元单元网格自动生成[J]. 河北建筑科技学院学报, 1998,15(4): 42-47.(GUO Yanhua, YANG Jianhui, WU Hao. Automatic generation of grids for two dimensional finite elements problems[J]. Journal of Hebei Institute of Architectural Science and Technology,1998,15(4): 42-47.(in Chinese))
    [10] 孙彩华. 传热学中的有限元法数值分析[J]. 青海师范大学学报(自然科学版), 2013(1): 31-34.(SUN Caihua. Numerical analysis of the finite element method in heat transfer[J]. Journal of Qinghai Normal University (Natural Science),2013(1): 31-34.(in Chinese))
    [11] SAGAWA T, UEDA M. Second law of thermodynamics with discrete quantum feedback control[J]. Physical Review Letters,2008,100(8): 080403. doi: 10.1103/PhysRevLett.100.080403.
    [12] 刘相华. 刚塑性有限元及其在轧制中的应用[M]. 北京: 冶金工业出版社, 1994.(LIU Xianghua. Rigid-Plastic Finite Element and Its Application in Rolling [M]. Beijing: Metallurgical Industry Press, 1994.(in Chinese))
    [13] 段鹏飞, 江增荣, 丁桦. 有限单元质量质心集中方法的探讨[J]. 力学与实践, 2010,32(4): 58-61.(DUAN Pengfei, JIANG Zengrong, DING Hua. The method of centroid lumped mass in the finite element[J]. Mechanics in Engineering,2010,32(4): 58-61.(in Chinese))
    [14] ILINCA F, Htu J F. Galerkin gradient least-squares formulations for transient conduction heat transfer[J]. Computer Methods in Applied Mechanics and Engineering,2002,191(27/28): 3073-3097.
    [15] 奥齐西克 M N. 热传导[M]. 俞昌铭, 译. 北京: 高等教育出版社, 1984.(ZISIK M N. Heat Conduction [M]. YU Changming, transl. Beijing: Higher Education Press, 1984.(Chinese version))
  • 加载中
计量
  • 文章访问数:  1167
  • HTML全文浏览量:  88
  • PDF下载量:  797
  • 被引次数: 0
出版历程
  • 收稿日期:  2017-06-13
  • 修回日期:  2017-09-25
  • 刊出日期:  2018-04-15

目录

    /

    返回文章
    返回